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A statement can be called valid, i.e. logical truth, in some systems of logic like in Modal logic if the statement is true in all interpretations. In Aristotelian logic statements are not valid per se. Validity refers to entire arguments. The same is true in propositional logic (statements can be true or false but not called valid or invalid).
The resolution rule in propositional logic is a single valid inference rule that produces a new clause implied by two clauses containing complementary literals. A literal is a propositional variable or the negation of a propositional variable.
Logic studies valid forms of inference like modus ponens. Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and ...
Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction ...
The systematic study of the form of valid inference, including the structures that allow or compel particular conclusions given certain premises. logic gate A physical device implementing a Boolean function, used in digital circuits to perform logical operations on one or more binary inputs to produce a single binary output. logical machine
The notion of valid argument is usually applied to inferences in arguments, but arguments reduce to propositional formulas and can be evaluated the same as any other propositional formula. Here a valid inference means: "The formula that represents the inference evaluates to "truth" beneath its principal connective, no matter what truth-values ...
Of the many and varied argument forms that can possibly be constructed, only very few are valid argument forms. In order to evaluate these forms, statements are put into logical form . Logical form replaces any sentences or ideas with letters to remove any bias from content and allow one to evaluate the argument without any bias due to its ...
Modus ponendo tollens (MPT; [1] Latin: "mode that denies by affirming") [2] is a valid rule of inference for propositional logic. It is closely related to modus ponens and modus tollendo ponens . Overview